Why does
the mirror
reflect you left-right, and not up-down?
Coxeter,
Ludwig Wittgenstein, and
E.C. Escher....

BEFORE YOU EMAIL ME:

UNT students: put the course name and main idea on the subject line!

UNT students: is the answer to your question in the syllabus?

I don't respond to emails about web development or coding, no thank you.

I don't respond to emails asking if I tutor students not enrolled in my courses; I don't.

Graduate students: nagging is allowed, sometimes encouraged.

Letters of recommendation: best ask 2-6 weeks before due date, more time is required if over a break.

I don't respond to emails asking about research/lab positions;
these go to PhD students in math at UNT.
Post-doc positions (assistant professor) are another story.

WHY MATH?
Saying mathematics is about numbers is like saying great literature is
about letters. Likewise, manipulating equations in mathematics is
about as important as manipulating grammar in literature.
Mathematics has more in common with arts and music than other
scientific fields: We imagine what could be possible and leave other
scientists to decide what fits the data. Indeed, many people
choose math because it requires more imagination than any other field
they have encountered. Math is also #1 in job satisfication according to JobRated.com. Undergrads: see Tom Forde's page.ALGEBRA
SEMINARPUBLICATIONSAWMThe American Women for
Mathematics organizes a workshop at the joint American Mathematical Society and Mathematical Association of America meetings each January, currently supported by an NSF AWM ADVANCE grant. Sarah Witherspoon and I organized the poster session Jan 2017 and the workshop Jan 2018 on Noncommutative Algebra and Representation Theorywith speakers:Chelsea Walton, Sian Fryer, Van Nguyen, Gordana Todorov, Elizabeth Drellich, Khrystyna Serhiyenko, Ellen Kirkman, Vyjayanthi Chari, Julia Plavnik, Natasha Rozhkovskaya, Pamela Harris, Monica Vazirani, Julia Pevtsova

Find a list of women (cis and trans) working in noncommutative algebra and representation theory here. TORAI'm on the steering committee and
organizer for conference
series

supported by the National Science Foundation and Oklahoma State University, University of Oklahoma, and University
of North Texas (UNT). Next meeting: TORA IX will take place Apr 7-8, 2018 at the University of Oklahoma.

Physicists often regard space as a Calabi-Yau manifold endowed
with symmetry. We model the local setting with a finite group G acting
linearily on a finite dimensional vector space V. We
mod out by symmetry to obtain the orbifold V/G which
may have singularities. Geometrically, we might replace V/G with a smooth
variety, but Hochschild cohomology recommends an algebraic approach:
replace the ring of invariant polynomials S^G with the
natural semi-direct product algebra S#G.
Hochschild
cohomology governs the deformation theory and
predicts various algebras important in representation theory,
combinatorics, and the geometry of orbifolds.

I also work with reflection
groups. These are groups (acting on a finite dimensional vector
space) generated by reflections: elements that fix a hyperplane
(or "mirror") pointwise. They include the Weyl and Coxeter groups,
complex reflection groups (u.g.g.r.'s), and reflection groups over
arbitrary fields. Their
study intertwines invariant theory and
arrangements of hyperplanes. (Scott
Crass can explain relations with Dynamical Systems.)

I attended the at Valparaiso University---a small,
liberal arts school in Indiana. I minored in the humanities,
co-founded a comedy troupe, participated in many theatre productions,
and worked for the music department as a piano accompanist.
I decided to major in math after participating in a Research Experience
for Undergraduates program at the University
of Oklahoma. I also spent a semester at Hangzhou University in
China (took Chinese language classes and also taught English at
the Y.M.C.A.). Afterwards, I moved to California for grad
school and scuba diving. Moray eels
provide nice examples for constructing orbifolds.
Maybe not the wolf
eel. And, in case you were wondering, the Mason and Hamlin BB is 212 cm long. And, yeah, it does sound really "fat". Especially with custom Isaac hammers (swoon).

Hyperbolic
Space:
Reflection groups and modular forms:

Images by Douglas Dunham (University
of Minnesota at Duluth), and Charlie Gunn with The Geometry Center
(Univ of Minnesota).

Coxeter says of Escher's print: "He
got it absolutely right to the millimetre, absolutely to the
millimetre. ... Unfortunately, he didn't live long enough to see my
mathematical vindication."